Since the introduction of Berkeley Spice in the early 1970's, circuit simulation has become an invaluable tool in the design of analog and digital circuits. It is common for modern designers to use circuit simulators not only to test designs before constructing them, but to optimize many circuit parameters. Spice is capable of DC, AC, and transient simulations of a wide variety of circuits. Many circuit simulators available today trace many of their features, including syntax and capabilities, to Spice, and several use algorithms derived from those of Spice. Common analog circuit simulators include Hspice, Pspice, and other Berkeley-Spice derivatives including Hpspice, Powerspice Ispice, Eldo, Ispec, Mtime, and Spectre.
Over recent decades, simulation models for active devices like transistors have become quite accurate and efficient even for the high-speed, small geometry, devices found in modem integrated circuits. Simulation models for ideal passive devices like resistors and capacitors are also efficient and accurate.
Real world circuits contain circuitry beyond active devices and ideal passive devices. Real circuits have internal and external interconnect that can be considered lossy transmission lines. Real transmission lines are typically lossy due to conductor resistances, including skin effect resistance, and dielectric losses. Transmission lines also have delay, and frequency-dependent reflections may arise because of impedance mismatches at ends of the transmission line. Accurate modeling and simulation of delay and reflections can be of great importance to circuit and system designers.
In the early days of integrated circuits, designers were able to ignore the lossy transmission line characteristics of internal interconnect. As circuit speed increased in recent years, it has become necessary to consider transmission line effects that historically were ignored.
It is therefore necessary to have a fast, efficient, accurate, lossy transmission line simulation model for circuit simulation of circuitry containing lossy transmission lines. It is also desirable that the simulation model function for DC, AC and transient simulations.
Some circuit simulators incorporate proprietary transmission line models. For example, the Hspice W element uses a set of proprietary algorithms for modeling transmission lines. The Hspice W element description of the transmission line characteristics is prepared in terms of frequency, the analysis by Spice during AC analysis is done in the frequency domain. This model does not readily transfer to the time domain, forcing use of a completely different algorithm for transient simulations. The Hspice W element therefore executes AC and transient simulations with separate algorithms. It is known in the industry that the W-Element had significant errors in the time domain algorithm for several years after its introduction. The Hspice W element transmission line is not found on most other simulators, circuit simulations that use them are not portable to those simulators.
It is desirable to model lossy transmission lines in a simple, fast, efficient, portable, and accurate way. To ensure portability, it is desirable that a transmission-line model be built from those circuit elements commonly found in Spice, Spice-derived, and Spice-like analog circuit simulators. It is also desirable that the model be implemented in Spice components that can be executed without alteration in AC and transient analysis.
Spice, Spice-like, and Spice-derived circuit simulators generally use the first character of each line of source to determine a component type. They provide primitives for the following component types:
First CharacterComponent TypeRResistorCCapacitorLInductorEVoltage Dependent Voltage SourceTIdeal (lossless) Transmission LineXSubcircuit invocationVVoltage sourceGVoltage Dependent Current SourceHCurrent Dependent Voltage Source
While Spice provides an integral transmission line model, this typically models an ideal, lossless, transmission line as opposed to a lossy transmission line.
A commonly used circuit model for lossy transmission lines is an R-L-C ladder. The R-L-C ladder model uses cells containing a resistor, an inductor, and a capacitor. For balanced transmission lines, each cell contains two resistors, two inductors, and a capacitor. The cell is repeated multiple times, repetition increases accuracy of the model. While an R-L-C ladder model can provide portability and, if sufficient cells are used, reasonable accuracy, it has drawbacks at higher frequencies. Lossy transmission lines have a complex frequency dependence which can be difficult to model with fixed, discrete elements. For good accuracy, each frequency dependent resistor in FIG. 1 may need to be modeled using as many as 30 elements. High frequencies demand many R-L-C sections for accuracy, so the component count of the model can become quite large. The geometry of the model can also generate an ill-conditioned matrix which can cause severe round-off errors in the Spice engine. Round-off errors are undesirable because, the Spice simulation loses accuracy and may fail to converge. Failure to converge causes simulation to cease, and data is lost beyond this point in the analysis. What is needed is a new approach to the modeling of lossy transmission lines that does not require a large number of elements, can be used for transient and frequency analysis, and can accommodate variable lengths and frequencies without requiring large numbers of elements.